Question: Simplify the following expression: $ q = \dfrac{-4}{9} - \dfrac{x + 6}{9} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-4}{9} \times \dfrac{9}{9} = \dfrac{-36}{81} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{x + 6}{9} \times \dfrac{9}{9} = \dfrac{9x + 54}{81} $ Therefore $ q = \dfrac{-36}{81} - \dfrac{9x + 54}{81} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-36 - (9x + 54) }{81} $ Distribute the negative sign: $q = \dfrac{-36 - 9x - 54}{81}$ $q = \dfrac{-9x - 90}{81}$ Simplify the expression by dividing the numerator and denominator by 9: $q = \dfrac{-x - 10}{9}$